报告题目：On a classification of steady solutions to two-dimensional Euler equations

报告人：澳门大学Gui Changfeng教授

时间：2024年12月12日14:00-15:00

腾讯会议号：149858676

In this talk, I shall provide a classification of steady solutions to two-dimensional incompressible Euler equations in terms of the set of flow angles. The first main result asserts that the set of flow angles of any bounded steady flow in the whole plane must be the whole circle unless the flow is a parallel shear flow. In an infinitely long horizontal strip or the upper half-plane supplemented with slip boundary conditions, besides the two types of flows appeared in the whole space case, there exists an additional class of steady flows for which the set of flow angles is either the upper or lower closed semicircles. This type of flows is proved to be the class of non-shear flows that have the least total curvature. As consequences, we obtain Liouville-type theorems for two-dimensional semilinear elliptic equations with only bounded and measurable nonlinearity, and the structural stability of shear flows whose all stagnation points are not infection points, including Poiseuille flow as a special case. Our proof relies on the analysis of some quantities related to the curvature of the streamlines. This talk is based on a joint work with Huan Xu and Chunjing Xie.

报告人简介：Gui Changfeng(桂长峰)教授，澳门大学数学系讲座教授，数学系主任，澳大发展基金会数学杰出学者，国家级人才项目获得者，博士生导师。1991年在美国明尼苏达大学获博士学位。桂长峰教授曾入选国家级人才计划和海外高层次人才，于2013年当选美国数学会首届会士，获得过IEEE最佳论文奖、加拿大太平洋数学研究所研究成果奖、加拿大数学中心Andrew Aisensdadt奖等荣誉。桂长峰教授现致力于非线性偏微分方程的研究，特别是在Allen-Cahn方程的研究、Moser-Trudinger不等式最佳常数的猜想、De Giorgi 猜想和Gibbons 猜想等方面取得了一系列在国际上有影响的工作，在Ann. of Math., Invent. Math., Comm. Pure Appl. Math.等国际顶级期刊上发表论文80余篇。